A suppressed edge is shared by two surfaces but it is ignored by the automesher.
Suppressed edges are colored blue by default.
Like a shared edge, a suppressed edge indicates geometric continuity between two surfaces but, unlike a shared edge, the automesher will mesh across a suppressed edge as if it were not even there. The automesher does not place seed nodes along the length of a suppressed edge and, consequently, individual elements will span across it. By suppressing undesirable edges you are effectively combining surfaces into larger logical meshable regions.